The study will bring mathematical and econometric tools to bear on the problem of extending and testing macro approaches to questions about the interdependencies of population and economic sectors of developed countries. A systematic comparison will be made of existing models of long run equilibrium growth with population endogenous to determine their comparative steady state solution features, their comparative sensitivity behavior under parameter change, and their out-of-steady state behavior. The latter, important analysis is based on the mathematical concept of a trend solution applied to a system of differential equations. Trend solutions get underway when structural relationships are affected by variables such as technological progress, opportunity costs of raising children, and behavioral changes with respect to saving, etc. Econometric tests of trend solutions will be carried out that will yield quantitative estimates of the macro-level economic parameters influencing economic growth. By means of these quantitative estimates, statistical tests will be made to relate variables to empirical patterns characteristic of the demographic transition. Quantitative estimates may be used for probabalistic prediction and appraisal of selected public policy proposals.